Compton scattering and momentum

In summary: You can try it, using my program, by just editing the values of p1, p2, p3.In summary, if a photon collides with an electron not moving, and you know the momentum of the photon before and after, and the electrons momentum, it is possible to know the direction of the electron and the photon after the collision. However, the situation may not have a solution if there is too much initial information and only two unknown quantities. To guarantee a solution, three unknown quantities are needed and can be found by using equations for conservation of momentum and energy.
  • #1
johann1301
217
1
If a photon collides with an electron not moving, and you know the momentum of the photon before and after, and the electrons momentum, is it possible to know the direction of the electron and the photon after the collision?
 
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  • #2
If you know the momentum of the electron and the photon _after_ the collision, then by definition you know their directions!

Momentum is a vector quantity!
 
  • #3
You only know only the absolute value of the momentum after the collision. You know the vector of the photon before.
 
  • #4
In general, your situation has no solution because it is over-specified: too much initial information, with only two unknown quantities.

[added later: see my next post below]

All of the momentum vectors lie in a plane, therefore we need to use only two components of momentum, e.g. x and y. We have three equations for conservation of x-momentum, y-momentum, and energy. In order to guarantee a solution, we need three unknown quantities.
 
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  • #5
If we know the momentum of e we know the Ke of e, and then we you know, by difference, the energy Es of the scattered photon ps.
If we know Es then we know the direction of ps and from this we can get the direction of e,
isn't it so?
 
  • #6
bobie said:
If we know the momentum of e we know the Ke of e, and then we you know, by difference, the energy Es of the scattered photon ps.

He already knows (is given) the momentum of the scattered photon, therefore he already knows its energy.

I just now noticed that he didn't say that he knows the momentum (or energy) of the incoming photon. If indeed he doesn't know that, then that is his third unknown quantity, and he can solve the momentum and energy conservation equations to find:

  • the momentum (and energy) of the incoming photon
  • the direction (angle) of the outgoing photon
  • the direction (angle) of the outgoing electron
 
  • #7
johann1301 said:
If a photon collides with an electron not moving, and you know the momentum of the photon before and after, and the electrons momentum, is it possible to know the direction of the electron and the photon after the collision?
jtbell said:
I just now noticed that he didn't say that he knows the momentum (or energy) of the incoming photon
It's complementary, jitbell, I missed the second bit and you the first.
The information he has is more than enough
 
  • #8
Oops, I missed the "before." Yes, he can use your procedure, provided that the three values of momentum are indeed consistent with conservation of energy (which he should confirm, as a first step).

If you give three "random" values for the momenta, in general they won't work because energy won't be conserved.
 

FAQ: Compton scattering and momentum

What is Compton scattering and how does it work?

Compton scattering is a phenomenon in which an incoming photon collides with an electron, causing the photon to lose energy and change direction. This change in energy and direction is due to the transfer of momentum from the photon to the electron. This process is described by the Compton scattering formula.

What is the significance of Compton scattering in physics?

Compton scattering is significant in physics because it provides evidence for the particle nature of light and the existence of photons. It also helps researchers to understand the behavior of electrons and their interaction with photons, which is important in fields such as quantum mechanics and particle physics.

How does Compton scattering affect the energy and wavelength of the scattered photon?

The energy and wavelength of the scattered photon are affected by the angle and energy of the incoming photon, as well as the mass and velocity of the electron. The scattered photon will have less energy and a longer wavelength compared to the incoming photon due to the transfer of energy and momentum to the electron.

Can Compton scattering be observed in everyday life?

Yes, Compton scattering can be observed in everyday life through processes such as X-ray imaging and medical procedures like CT scans. These techniques use the principles of Compton scattering to create images of the internal structures of objects, including the human body.

How is momentum conserved in Compton scattering?

Momentum is conserved in Compton scattering by the transfer of momentum from the incoming photon to the electron. This allows for the calculation of the change in momentum of the scattered photon and the electron, which must be equal and opposite to satisfy the law of conservation of momentum.

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